Skip to Main content Skip to Navigation
Theses

Reidemeister torsion on character varieties

Abstract : In this PhD dissertation, we study a topological invariant of 3-manifolds, namely the Reidemeister torsion, as globally defined on character varieties of the fundamental group in SL(2,C). The « adjoint » torsion will be the torsion of the cohomological complex associated to the adjoint representation. We explain that it can be seen as a meromorphic differential form on the character variety, and we aim to understand its poles and zeros. They will be related with -singular points of the character variety -the topology of incompressible surfaces embedded in the 3-manifold, provided by the Culler-Shalen theory. As an application, we prove a relation between the genus of those incompressible surface and the genus of the character variety. The « acyclic » torsion of the standard complex is a rational function on the character variety. We study its poles at infinity in the character variety, and we give sufficient conditions for this torsion to be non constant.
Document type :
Theses
Complete list of metadatas

Cited literature [60 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02108892
Contributor : Abes Star :  Contact
Submitted on : Wednesday, April 24, 2019 - 2:31:26 PM
Last modification on : Friday, August 21, 2020 - 5:43:08 AM

File

2018SORUS020.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-02108892, version 1

Citation

Léo Bénard. Reidemeister torsion on character varieties. Algebraic Topology [math.AT]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS020⟩. ⟨tel-02108892⟩

Share

Metrics

Record views

105

Files downloads

132